The EU referendum must be “rerun” after the official Brexit campaign was found to have breached spending laws by the elections watchdog, MPs have said.

The Electoral Commission has referred David Halsall, the “responsible person” for Vote Leave, to the police for making false declarations of campaign spending, after it was found to have coordinated illegally with Brexit youth group BeLeave.

Darren Grimes, head of BeLeave – which received a £675,000 donation from Vote Leave – has also been referred to the police.

If the gift had been recorded as part of Vote Leave’s referendum expenditure, it would have taken the campaign’s spending over the £7m limit, the commission said.

Senior Conservative MP Sarah Wollaston said Vote Leave had been involved in “deliberate cheating” during the 2016 referendum campaign, which cast doubt on the Brexit result in the minds of the public.

Tory grandee Sir Nicholas Soames called for the electoral system to be “blown up and started all over again” in the wake of the “gross” findings by the Electoral Commission.

The watchdog said it found “significant evidence” of joint working between Vote Leave – which was fronted by Michael Gove and Boris Johnson – and BeLeave.

Speaking during an urgent question in the Commons, Dr Wollaston said: “Consequences must follow, we cannot have confidence that this referendum was secure and it should be rerun.”

Sir Nicholas said the voting and democratic system was once one of the UK’s greatest assets.

He said: “One of the great glories of this sadly now diminished country was our electoral and democratic system, and this example today is gross.

“And I say to her [Cabinet Office minister Chloe Smith], that if we are to retain the integrity and the trust of the voting public, the whole damn thing needs to be blown up and started all over again.”

Former home secretary Amber Rudd urged the minister not to let the efforts to deliver the referendum result to “obfuscate from the real questions that are being raised here”.

The criticism was led by Labour MP Chuka Umunna, who said Vote Leave’s actions were an “affront to our democracy” and called for a public inquiry.

“Given there was a 4 per cent gap between Leave and Remain, and VoteLeave overspent by just under 8 per cent, does the minister agree with me that we cannot say with confidence that this foul play did not impact on the result,” he said.

Mr Umunna added: “Members of the cabinet sat in an organisation which has been found to have flouted our democracy.

“Does this not all demonstrate that we need a full, urgent public inquiry into the Leave campaign, given that it calls into question the legitimacy of the whole Brexit process, which is preoccupying this House.”

Labour’s David Lammy also backed calls for a rerun and urged ministers to declare the referendum result as “void”.

He said: “Can the government declare this referendum void on the basis of the evidence that we’ve been provided by the Electoral Commission, and if not, given this was an advisory referendum, can she bring forward the vote in this parliament to declare this referendum void?”

MPs also demanded action against several high-profile Tories who were involved in Vote Leave, including Mr Gove, the environment secretary, and ex-foreign secretary Mr Johnson.

Shadow cabinet office minister Christian Matheson said both politicians needed to explain their role in the “initial scandal and the cover-up”, and questioned if they would be referred to the cabinet secretary over whether they had breached the ministerial code.

The SNP’s Tommy Sheppard echoed his concerns and said anyone involved should be taken off the government payroll.